Quantum crossing symmetry as heart of ghost imaging

In this paper it is proved that the keys to understanding the ghost imaging are the crossing symmetric (CS) photon reactions in the nonlinear media. So CS introduced a real optical path between the object and his “ghost” image, making possible to apply the geometric optics for a rigorous proof of the essential laws of the “ghost” imaging phenomena. Hence, the laws of the plane quantum mirror (QM) and that of spherical quantum mirror, observed in the ghost-imaging experiments, are shown that can be obtained as natural consequences of the energy-momentum conservation laws. So, it is proved that the ghost imaging laws depend only on the energy-momentum conservation and not on the photons entanglement. Using DFG-typical features we obtained explicit predictions of the intensities of the idler photons in terms of the intensities of the interacting photon-(p and s)-beams in the nonlinear crystal. Two fundamental experiments for a decisive test of the [SPDC-DFG]-quantum mirrors are suggested.